RANDOM-WALK CONSTRUCTION OF SPINOR FIELDS ON A 3-DIMENSIONAL LATTICE

Euclidean-invariant Klein-Gordon, Dirac and massive Chem-Simons field theories are constructed in terms of a random walk with a spin factor on a three-dimensional lattice. We exactly calculate the free energy a nd the correlation functions which allow us to obtain the critical dif fusion constant and associated critical exponents. It is pointed out t hat these critical exponents do not satisfy the hyper-scaling relation but the scaling inequalities. We take the continuum limit of this the ory on the basis of these analyses. We check the universality of the o btained results on other lattice structures such as the triclinic latt ice and the body-centered lattice.